Statistical Analysis Guidelines
Regression Analysis
After calculating the mean measured value for each concentration level, a best-fit straight line is fitted through the data using linear regression. The regression line is the statistical model for what the measurement procedure predicts at each expected concentration:
Design A1 — Regression Through Origin
Y = A × E (no intercept)
For dilution studies, the regression line is forced through the origin (0, 0) because a measurand-free sample (Blank) should produce a measured value of zero. Fitting without an intercept ensures that proportionality — the defining property of linearity — is directly tested. The estimated slope A should be close to 1.0 for a well-performing measurement procedure.
Design A3 — Standard Linear Regression
Y = A × E + B (with intercept)
For assigned-value studies, a standard linear regression with intercept is used. The slope reflects proportional response, and the intercept captures any fixed additive offset. The module uses weighted least squares (WLS) regression when SD increases with concentration (as is typical), giving lower-concentration levels less influence over the fit than their higher-concentration counterparts.
The regression produces the following output for each study:
Regression Slope
Rate of change in measured values per unit of expected value. Slope close to 1.0 indicates proportional agreement; significant deviation indicates proportional bias.
Regression Intercept (A3)
The estimated measured value when the expected value is zero. A non-zero intercept indicates a constant offset across the measurement range.
Estimate (Predicted Value)
For each level: Estimate = Slope × Expected Value (A1) or Slope × Expected Value + Intercept (A3). This is the value the regression line predicts at that concentration.
Correlation Coefficient (r)
Measures the strength of the linear relationship between expected and measured values. Values close to 1.0 indicate a strong linear relationship.
Residuals and Pass/Fail Criteria
For each concentration level, the residual is the difference between the measured mean and the regression-predicted (estimated) value. It quantifies how far the actual measurement deviates from what a perfectly linear method would produce:
Residual
Residual = Measured Mean − Estimate (Predicted Value)
A residual close to zero means the measurement procedure performs as predicted by the regression line at that concentration. Large residuals indicate nonlinear behavior at that level. The sign indicates direction: a positive residual means the measured value exceeds the prediction, while a negative residual means the measured value falls below it.
Systematic Error Allowance (SEa)
SEa = TEa × (Bias Allocation % / 100)
The SEa defines the tolerance window around the regression line within which residuals must fall to pass linearity. It is derived from the Total Allowable Error (TEa) by applying the configured bias allocation percentage — the fraction of the TEa budget assigned to systematic error (bias). For example, TEa = ±8% with a 25% bias allocation gives SEa = ±2%.
A concentration level passes linearity if its residual falls within the SEa tolerance. How the residual is compared against the SEa depends entirely on the TEa format configured for the assay. Legion Diagnostics supports multiple TEa formats, and the pass/fail evaluation method mirrors whichever format is in use:
| TEa Format | Example | Pass Criterion |
|---|---|---|
| Percentage (all concentrations) | ±8% | |% Residual| ≤ SEa% at every level |
| Absolute (all concentrations) | ±5 mg/dL | |Residual| ≤ SEa (absolute) at every level |
| Greater of absolute or % | ±5 mg/dL or ±8% (whichever is greater) | Residual compared against whichever SEa value is larger at that level |
| Concentration-dependent: abs low / % high | ±5 mg/dL if ≤ 20 mg/dL or ±8% if > 20 mg/dL | |Residual| ≤ abs SEa below threshold; |% Residual| ≤ % SEa above threshold |
| Concentration-dependent: % low / % high | ±6% if ≤ 50 mg/dL or ±10% if > 50 mg/dL | |% Residual| ≤ lower SEa% below threshold; |% Residual| ≤ upper SEa% above threshold |
| Concentration-dependent: abs low / abs high | ±3 mg/dL if ≤ 20 mg/dL or ±8 mg/dL if > 20 mg/dL | |Residual| ≤ lower abs SEa below threshold; |Residual| ≤ upper abs SEa above threshold |
| Concentration-dependent: greater-of low / % high | ±3 mg/dL or ±6% (greater) if ≤ 20 mg/dL or ±10% if > 20 | Greater-of logic below threshold; % SEa above threshold |
| Concentration-dependent: % low / greater-of high | ±6% if ≤ 50 mg/dL or ±5 mg/dL or ±10% (greater) if > 50 | % SEa below threshold; greater-of logic above threshold |
| Concentration-dependent: greater-of low / greater-of high | ±3 mg/dL or ±6% (greater) if ≤ 20 mg/dL or ±8 mg/dL or ±12% (greater) if > 20 | Greater-of logic applied independently below and above threshold |